adding a siren to a factory alarm

Your best bet would be to find the wiring diagram for the alarm system.  Some cars have seperate circuits for the alarm horn output and the steering wheel horn output, but some cars use the same circuit.

If it does use the same circuit you could wire a relay up to prevent the siren from sounding if the ignition is on - that might be good enough.  You may also be able to tap in to the steering wheel horn switch (most are low current (-) signals that drive relays or BCMs) and prevent the siren from sounding whenever the steering wheel horn switch is pushed down.

the previous post is an easy enough solution, you can also try adding a capicitor to the siren to keep it on during the gaps in the horn honks so as the horn is honking, the siren remains constant throughout. There's a diagram on here for cornering lights (to turn on and stay on with intermitent turn signal) that should work for this.